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The expression in your image shows a limit as \( x \to \infty \). Specifically, it looks like the limit you're interested in is:

\[
\lim_{x \to \infty} \frac{e^t}{t}
\]

However, the variable \( t \) is unclear, as it might represent a parameter or be involved in the limit process. Assuming that \( t \) is independent of \( x \), and you're simply taking the limit as \( x \to \infty \) of a function that only involves \( t \), this limit might require additional clarification.

Could you confirm if \( t \) is a constant, or clarify the role of \( t \) in this limit process? This will help ensure the correct interpretation of your expression.

Would you like further details or have any questions about the limit process? 

Here are five questions that could expand on this concept:
1. What is the definition of a limit at infinity?
2. How do limits involving exponential functions behave as \( x \to \infty \)?
3. Can you describe the behavior of the function \( \frac{e^t}{t} \) as \( t \to \infty \)?
4. What are the key techniques for solving limits involving indeterminate forms like \( \frac{\infty}{\infty} \)?
5. How does L'Hopital's Rule help in evaluating limits involving quotients?

**Tip:** When dealing with limits involving exponential functions, knowing how the exponential growth compares with other functions (like polynomials) is crucial in determining the behavior of the expression.

What is the limit as x approaches infinity of e^t / t?

Explore the limit of the function e^t/t as x approaches infinity. Learn key concepts such as the behavior of exponential growth and L'Hopital's Rule to evaluate indeterminate forms. Suitable for college-level calculus students.

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